Productive physical investment and growth: testing the validity of the AK model from a panel perspective

Abstract

In this article, we analyse the relationship between productive physical investment and economic growth from a panel perspective for a sample of 61 countries spanning the period 1950 to 1992. The analysis can be thought of as two-fold. First, we test the empirical validity of AK models following the logic by Jones (1995). For that purpose, we determine the degree of persistence of physical investment rates and growth by employing recently developed panel unit-root tests that enable us to make more reliable inferences about the existence of stochastic trends in the series. Second, we estimate the long-run effect of physical investment on growth by using panel data techniques rather than cross-section regressions. Overall, our findings cast doubts on the rejection of the empirical validity of the AK model, as suggested by Jones’ analysis.

Acknowledgement

The author would like to thank seminar participants at the University of Exeter. Special thanks go to Simon Wren-Lewis, Richard Harris and Jonathan Temple for detailed and valuable comments and two anonymous referees for suggestions that led to a substantial improvement of the article. I am also indebted to participants at the New Developments in Macroeconomic Modelling and Growth Dynamics Conference held in Faro, Portugal and particularly Tony Thirlwall, for helpful suggestions. Financial support from the Spanish Ministry of Education and Science under grant number SEJ2006-04803/ECON is gratefully acknowledged.

Notes

¹For an authoritative review of the empirics of growth including the main studies in the field and the methodological as well as econometric problems, see Temple (1999).

²McGrattan (1998) does not estimate autoregressive distributed lag growth models in order to establish the existence of a positive long-run link between growth and physical investment, as suggested by AK models. Rather, she reports some descriptive evidence through a scatter plot showing a positive relationship between average investment rates and average growth rates for a large cross-section of countries. But this procedure fails to control for the likely endogeneity of investment rates and for the dynamics in the investment-growth nexus.

³The list of the countries is provided in the Appendix. The full sample consists of 61 countries for which disaggregated data on investment were available. Detailed descriptive statistics of the data used throughout the analysis are provided in the Appendix (Table A1).

⁴Panel unit-root tests constitute a more efficient way to increase statistical power than employing univariate unit-root tests with GLS-de-trending as previously done in Romero-Ávila (2006).

⁵We have refrained from using the recently released Penn World Table version 6.1, since it does not provide disaggregated data on investment shares.

⁶Such correction factors are provided in IPS for different degrees of lag-length augmentation and sample sizes in the time dimension.

⁷This condition constitutes an important advantage over other tests such as Levin et al. (2002) where N/T must tend to zero as N and T grow large for the validity of the test.

⁸The degree of augmentation for the individual ADF specifications were computed following the general-to-specific step-down procedure by which it is necessary to remove insignificant lag-differenced terms until the last term is significant at conventional levels of significance.

⁹As pointed out by Jones (1995), any macroeconomic variable expressed as a share of GDP, such as physical investment shares cannot be driven by a pure unit-root process, since they are bounded between zero and one, and a stochastic process characterized by a pure unit root would cross such bound sooner or later. However, the investment share can be conceivably driven by a stochastic trend within the interval comprised between zero and one.

¹⁰Note that the inferences we could draw on the basis of the panel unit-root tests for the total investment share would remain the same: a clear nonrejection of AK models.

¹¹These distributed lag models can be safely applied to the estimation of regressions with stationary variables.

¹²See for instance the AK model of Barro and Sala-i-Martin (1995, Chapter 4) that focuses on total physical and human capital accumulation.

¹³This practice is similar to the approach by Stock and Watson (1993), who propose the dynamic ordinary least squares estimator (DOLS), which corrects for the endogeneity of regressors and serially correlated errors by using leads of the regressors in first-differences.

¹⁴The results appear fairly similar when different lag and lead lengths are used in the computations. In order to keep a reasonable number of degrees of freedom, we set to six and five the number of lags and leads included in the regressions.

¹⁵The inclusion of time dummies can be an additional way of controlling for common third factors that may drive both investment and output over the cycle.

¹⁶As noted by Karras (1999) and Evans (1997), if the growth rate of per capita output is stationary around a trend, the distributed lag models we have presented so far may be mis-specified by not allowing for a deterministic trend in the set of regressors. As a robustness check, we re-estimated models (1)–(4) by also including a deterministic trend, which is assumed to be homogeneous across countries. The coefficients are similar to those of Table 3 and are available from the author upon request.

¹⁷De Long and Summers make use of saving rates and an orthogonalized equipment price to instrument for equipment investment. Nevertheless, Temple (1998) casts doubts on the validity of such instruments.

¹⁸It is important to note that data series are not first-differenced, since we do not have the problem induced by the correlation of individual country effects and the lagged dependent variable, as our model assumes away cross-country fixed effects. We follow Griliches and Miaresse (1995) and Temple (1998), who point out the pervasive effects of removing the between variability of the data. A further argument for not first differencing the data is that we could lose valuable information regarding the long-run link between productive investment and growth.

¹⁹We choose the lag-length of the instruments in a way that we can correct for the possibility of measurement errors in the investment shares in durables and nonresidential construction. See more details in Bond et al. (2001)

²⁰For notation purposes, models (5B) and (6B) differ from models (5A) and (6A), respectively in that they control for distributed lags of output growth. In turn, models (5A) and (5B) are estimated using the instruments proposed by Arellano and Bond (1991); and models (6A) and (6B) are estimated following Arellano and Bover (1995).

²¹See Arellano and Bond (1991), for details on the construction of the tests.

²²See Judson and Owen (2000), among others.

²³The instrumental variable estimations were carried out with the module called DPD available in the software PcGive.10 ©.

²⁴These countries are Iran, Botswana, Swaziland, Zambia, Luxembourg, Iceland and Venezuela. The reason is that oil-producer countries invest in productive capital for the extraction of fuel on the basis of external factors, such as, world growth prospects and world prices movements. Countries like Botswana rich in natural resources have an investment function also driven by external factors, such as the expectation about the movement of world prices of diamonds.